##
**Reduced 2D/1D mathematical models for analyzing inductive effects in submerged arc furnaces.**
*(English)*
Zbl 1481.78014

Summary: Mathematical models have been developed to investigate the quantitative behaviour of the current and power distributions in large submerged arc furnaces, usually fed by a low-frequency alternating source. Reduced 2D and 1D models will be used to investigate the electrical behaviour inside the furnace; in particular, these models will allow us to explain the inductive effects between the different regions and to compare the use of genuine AC models vs. DC approximations. The merits and limitations of the reduced models will be analyzed in terms of geometrical and physical parameters. The models are based on three-phase submerged arc furnaces for ferromanganese production, which are characterized by coke enriched regions (coke beds) under the electrodes. Mathematical analysis and computer simulations show how AC differs from the simpler direct current (DC). If the electrode-electrode distance is large, the current will mainly run horizontally between the electrodes. The unidimensional AC model shows that the distribution in the coke bed is largely influenced by the (parallel) currents in the metal. On the other hand, the corresponding DC model will predict constant current and power distributions here. Two-dimensional simulations reveal that this AC property will be preserved qualitatively also for realistic electrode-electrode distances. Hence, if there is a significant power contribution from horizontal currents in the coke bed (or slag), DC models should be avoided.

### MSC:

78A55 | Technical applications of optics and electromagnetic theory |

78-10 | Mathematical modeling or simulation for problems pertaining to optics and electromagnetic theory |

### Keywords:

metallurgy; submerged arc furnaces; induction; proximity effects; analytical 1D models; dimensional aanalysis### Software:

MaxFEM
PDF
BibTeX
XML
Cite

\textit{M. Fromreide} et al., Appl. Math. Modelling 98, 59--70 (2021; Zbl 1481.78014)

Full Text:
DOI

### References:

[1] | Halvorsen, S. A.; Olsen, H. A.H.; Fromreide, M., An efficient simulation method for current and power distribution in 3-phase electrical smelting furnaces, IFAC-PapersOnLine, 49, 20, 167-172 (2016) |

[2] | Sheng, Y. Y.; Irons, G. A.; Tisdale, D. G., Transport phenomena in electric smelting of nickel matte: part II, mathematical modeling, Metall. Mater. Trans. B, 29.1, 85-94 (1998) |

[3] | Dhainaut, M., Simulation of the electric field in a submerged arc furnace, Proceedings of the Tenth International Ferroalloy Congress, 605-613 (2004) |

[4] | Darmana, D.; Olsen, J. E.; Tang, K.; Ringdalen, E., Modelling concept for submerged AC furnaces, Proceedings of the Ninth International Conference on CFD in the Minerals and Process Industries, Melbourne, Australia (2012) |

[5] | Karalis, K. T.; Karkalos, N.; Cheimarios, N.; Antipas, G. S.E.; Xenidis, A.; Boudouvis, A. G., A CFD analysis of slag properties, electrode shape and immersion depth effects on electric submerged arc furnace heating in ferronickel processing, Appl. Math. Model., 40, 21-22, 9052-9066 (2016) · Zbl 07163308 |

[6] | Karalis, K.; Karkalos, N.; Antipas, G. S.E.; Xenidis, A., Pragmatic analysis of the electric submerged arc furnace continuum, R. Soc. Open Sci., 4 (2017) · Zbl 07163308 |

[7] | K. Karalis, N. Karkalos, G.S.E. Antipas, A. Xenidis, Computational fluid dynamics analysis of a three-dimensional electric submerged arc furnace operation, 10.31219/osf.io/xgnse, last access 1.dec.2020. · Zbl 07163308 |

[8] | Tesfahunegn, Y. A.; Magnusson, T.; Tangstad, M.; Saevarsdottir, G., Effect of electrode shape on the current distribution in submerged arc furnaces for silicon production - a modelling approach, J. South Afr. Inst. Min. Metall., 118, 595-600 (2018) |

[9] | McDougall, I., Finite element modelling of electric currents in AC submerged arc furnaces, Infacon XI: International Ferro-Alloys Congress, New Delhi, India (2007) |

[10] | Herland, E. V.; Sparta, M.; Halvorsen, S. A., 3D-models of proximity effects in large FeSi and FeMn furnaces, J. South Afr. Inst. Min. Metall., 118, 607-618 (2018) |

[11] | Herland, E. V.; Sparta, M.; Halvorsen, S. A., Skin and proximity effects in electrodes and furnace shells, Metall. Mater. Trans. B, 50, 2884-2897 (2019) |

[12] | Tesfahunegn, Y. A.; Magnusson, T.; Tangstad, M.; Saevarsdottir, G., Dynamic current and power distributions in a submerged arc furnace, (Lambotte, G.; Lee, J.; Allanore, A.; Wagstaff, S., Materials Processing Fundamentals 2019. Materials Processing Fundamentals 2019, The Minerals, Metals & Materials Series (2019), Springer) |

[13] | Tesfahunegn, Y. A.; Magnusson, T.; Tangstad, M.; Saevarsdottir, G., Comparative study of AC and DC solvers based on current and power distributions in a submerged arc furnace, Metall. Mater. Trans. B, 51, 510-518 (2020) |

[14] | Olsen, S. E.; Tangstad, M.; Lindstad, T., Production of Manganese Ferroalloys (2007), Tapir Academic Press |

[15] | Eidem, P. A., Electrical Resistivity of Coke Beds (2008), Norwegian University of Science and Technology, Ph.D. thesis |

[16] | Wasbø, S. O., Ferromangenese Furnace Modelling Using Object-Oriented Principles (1996), Norwegian University of Science and Technology, Ph.D.thesis |

[17] | Bossavit, A., Computational Electromagnetism (1998), Academic Press Inc: Academic Press Inc San Diego, CA · Zbl 0945.78001 |

[18] | Bermúdez, A.; Gómez, D.; Salgado, P., Mathematical Models and Numerical Simulation in Electromagnetism (2014), Springer International Publishing · Zbl 1304.78001 |

[19] | C. Multiphysics, AC/DC module user’s guide, v 5.4, 2018. |

[20] | Schlanbusch, R.; Halvorsen, S. A.; Shinkevich, S.; Gómez, D., Electrical Scale-up of Metallurgical Processes (2014), COMSOL Conference: COMSOL Conference Cambridge, UK |

[21] | Deng, H. W.; Zhao, Y. J.; Liang, C. J.; Jiang, W. S.; Jing, Y. M., Effective skin depth for multilayer coated conductor, Prog. Electromagn. Res. M, 9, 1-8 (2009) |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.